The proliferation of telecommunications based on optical fibers and other high-speed links that employ very high modulation frequencies has led to an increased demand for highly-precise and stable local frequency standards capable of operating outside the standards laboratory. Quartz crystals are the most commonly-used local frequency standard, but in many cases are not sufficiently stable to meet the stability requirements of modern, high-speed communications applications and other similar applications.
To achieve the stability currently required, a frequency standard requires a frequency reference that is substantially independent of external factors such as temperature and magnetic field strength. Also required is a way to couple the frequency reference to an electrical signal that serves as the electrical output of the frequency standard. Potential frequency references include transitions between quantum states in atoms, ions and molecules. However, many such transitions correspond to optical frequencies, which makes the transition difficult to couple to an electrical signal.
Transitions between the levels of certain ions and molecules and between the hyperfine levels of certain atoms have energies that correspond to microwave frequencies in the 1 GHz to 45 GHz range. Electrical signals in this frequency range can be generated, amplified, filtered, detected and otherwise processed using conventional semiconductor circuits.
An early example of a portable frequency standard based on an atomic frequency reference is the model 5060A frequency standard introduced by the Hewlett-Packard Company in 1964. This frequency standard used a transition between two hyperfine levels of the cesium-133 atom as its frequency reference, and had a frequency accuracy of about two parts in 10.sup.11. Current versions of this frequency standard have an accuracy of about five parts in 10.sup.13 and a stability of a few parts in 10.sup.14.
Less accurate but smaller frequency standards have been built that use a transition between the hyperfine states of a quantum absorber such as a rubidium-87 atom as their frequency reference. This type of frequency standard includes a cell filled with a vapor of rubidium-87 atoms and located in a microwave cavity. The rubidium atoms in the cell are illuminated with light from a rubidium lamp. The light generated by the lamp includes two spectral lines, one of which is filtered out by passing the light through an auxiliary cell filled with rubidium-85 atoms, so that light of essentially only a single frequency illuminates the rubidium atoms.
The rubidium-87 atom has a ground state, the S state, that is split into two groups of states by the hyperfine interaction between the magnetic moments of the electron and nucleus. Each group contains a number of sublevels. The two groups are separated by an energy corresponding to a frequency of about 6.8 GHz. At room temperature, all the sublevels in the groups are approximately equally populated. The first excited state, a P state, is also split by the hyperfine interaction but the splitting is much smaller and can be neglected for the purposes of this discussion. The P state is essentially unpopulated at room temperature. When the rubidium atoms are illuminated with the light from the rubidium lamp/filter cell combination, the light is absorbed since its frequency corresponds to the energy difference between the P state and one of the groups constituting the S state. The light absorption decreases the population of one of the groups constituting the S state and increases the population in the other. As the resulting population imbalance reaches equilibrium, absorption of the incident light decreases.
For convenience, the two groups into which the ground state S of the rubidium-87 atom is split by hyperfine interaction will from now on be called the ground states of the rubidium atom. Feeding microwave energy into the microwave cavity at a frequency of about 6.8 GHz, corresponding to the energy difference between the two ground states, tends to equalize the populations of the states. The change of population causes the absorption of the light transmitted through the cell to increase. This can be detected and the resulting detection signal used to control the microwave frequency to a frequency at which the absorption of the light transmitted through the cell is a maximum. When this condition is met, the microwave frequency corresponds to, and is determined by, the energy difference between the ground states. The microwave signal, or a signal derived from the microwave signal, is used as the frequency standard.
The energy difference between the two ground states is relatively insensitive to external influences such as electric field strength, magnetic field strength, temperature, etc., and corresponds to a frequency that can be handled relatively conveniently by electronic circuits. This makes the energy difference between the ground states a relatively ideal frequency reference for use in a frequency standard. However, in the type of frequency standard just described, interaction between the incident light and the rubidium atoms results in a.c. Stark shift. The a.c. Stark shift changes the energy difference between the ground states, and, hence changes the frequency of the microwave signal. Thus, the a.c. Stark shift reduces the accuracy of the frequency standard. Moreover, since the a.c. Stark shift depends, in part, on the intensity and frequency of the incident light, the a.c. Stark shift converts variations in the intensity and frequency of the incident light into variations in the frequency of the signal generated by the frequency standard. Thus, the a.c. Stark shift additionally reduces the stability of the frequency standard.
The type of frequency standard just described suffers from a number of additional disadvantages. For example, the microwave cavity in which the cell is located and the auxiliary filter cell make the frequency standard complex and expensive to manufacture.
More recently, frequency standards have been proposed that use as their frequency reference coherent population trapping (CPT) in the transition between the hyperfine states of a quantum absorber such as the rubidium-87 atom. The structure of the CPT-based frequency standard can be similar to that of the frequency standard just described, but the CPT-based frequency standard lacks an auxiliary cell and a rubidium lamp, and only needs a microwave cavity if coherent emission, described below, is detected. The cell is illuminated with incident light having two main frequency components in the near infra-red. The incident light can be generated using two phase-locked lasers or by modulating the frequency of a single laser. In the former case, the frequency difference between the main frequency components is determined by the frequency difference between the lasers. In the latter case, the frequency difference, between the main frequency components is determined by the modulation frequency applied to the laser.
The frequency difference is controlled to match the frequency corresponding to the energy difference between the two ground states to establish a specific coherence between the ground states, i.e., a condition in which the atoms are in a specific superposition of the ground states. The atoms in this specific superposition of the ground states do not interact with the two main frequency components in the incident light. This leads to the name dark state for the specific superposition of the ground states. The atoms in the dark state also have an oscillating electromagnetic multipole moment at a frequency equal to the frequency difference. The oscillating electromagnetic multipole moment emits an electromagnetic field called coherent emission. When the number of atoms in the dark state reaches a maximum, absorption of the incident light is minimized, transmission of the incident light through the cell is maximized and the fluorescent light generated as a result of the quantum absorber absorbing the incident light is minimized. Also, the coherent emission generated by the quantum absorber's oscillating electro-magnetic multipole moment is maximized.
The coherence condition between the ground states is detected by detecting the portion of the incident light that remains unabsorbed after passing through the quantum absorber, by detecting the fluorescent light generated by the quantum absorber in response to the incident light or by detecting the coherent emission generated by the quantum absorber in response to the incident light. The resulting detection signal is used to control the frequency difference or modulation frequency to a frequency at which the unabsorbed portion of the incident light has a maximum intensity, the fluorescent light generated by the quantum absorber has a minimum intensity or the coherent emission generated by the quantum absorber has a maximum intensity. When the coherence condition is met, the frequency difference or the modulation frequency (or a harmonic thereof) corresponds to, and is determined by, the energy difference between the ground states.
An exemplary CPT-based frequency standard is described by Normand Cyr, Michel Tetu and Marc Breton in All-Optical Microwave Frequency Standard: a Proposal, 42 IEEE TRANS. ON INSTRUMENTATION & MEASUREMENT, 640 (1993 April). Cyr et al. describe a practical example of a frequency standard that uses a single laser that emits light having a wavelength of 780 nm. The light is frequency modulated at a modulation frequency of 1.139 GHz, one-sixth of the frequency difference of 6.835 GHz corresponding to the energy difference between the ground states of rubidium-87. Cyr et al. disclose setting the modulation index of the frequency modulation to 4.2 to maximize the intensities of the main frequency components having frequencies corresponding to the transitions. The modulation index is the ratio of the deviation in the frequency of the light to the modulation frequency.
In the process of generating CPT, the frequencies of the main frequency components of the incident light are approximately equal to the frequencies corresponding to the two transitions of the quantum absorber. When the first main frequency component is not forbidden by selection rules from connecting one of the ground states to the excited state, it will cause energy shifts, called a.c. Stark shifts, in the other ground state and the excited state. Similarly, the second main frequency component will cause energy shifts, i.e., a.c. Stark shifts, in the one ground state and the excited state, if not forbidden. In a CPT-based frequency standard, the total a.c. Stark shift degrades the accuracy of the frequency standard while variations in the total a.c. Stark shift degrade frequency stability. The total a.c. Stark shift due to the above-described de-tuned frequency components makes the measured energy difference between the ground states significantly different from the unperturbed energy difference between these states.
Thus, what is needed is a CPT-based frequency standard that has a substantially reduced total a.c. Stark shift. A reduced total a.c. Stark shift is required to provide the frequency stability required for modern, high-speed communications and similar applications.